%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN087+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:57:51 PM UTC 2025 % Result : Theorem 6.62s 6.78s % Output : Proof 6.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN087+2 : TPTP v9.2.0. Released v7.3.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 11:40:23 EDT 2025 % 0.13/0.34 % CPUTime : % 6.62/6.78 SZS status Theorem for theBenchmark.p % 6.62/6.78 SZS output start Proof for theBenchmark.p % 6.62/6.78 Clause #0 (by assumption #[]): Eq (Exists fun Y24 => ∀ (X19 : Iota), Or (And (Not (r1 X19)) (Ne X19 Y24)) (And (r1 X19) (Eq X19 Y24))) True % 6.62/6.78 Clause #8 (by assumption #[]): Eq % 6.62/6.78 (∀ (X5 : Iota), % 6.62/6.78 Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 X5 Y17 Y8)) (Exists fun Y18 => And (r1 Y18) (Eq Y8 Y18))) % 6.62/6.78 True % 6.62/6.78 Clause #11 (by assumption #[]): Eq (Not (Exists fun Y1 => And (Exists fun Y2 => And (r1 Y2) (r4 Y2 Y2 Y1)) (Exists fun Y3 => And (r1 Y3) (Eq Y1 Y3)))) % 6.62/6.78 True % 6.62/6.78 Clause #30 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (X19 : Iota), Or (And (Not (r1 X19)) (Ne X19 (skS.0 2 a))) (And (r1 X19) (Eq X19 (skS.0 2 a)))) True % 6.62/6.78 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Or (And (Not (r1 a)) (Ne a (skS.0 2 a_1))) (And (r1 a) (Eq a (skS.0 2 a_1)))) True % 6.62/6.78 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Ne a (skS.0 2 a_1))) True) (Eq (And (r1 a) (Eq a (skS.0 2 a_1))) True) % 6.62/6.78 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (And (r1 a) (Eq a (skS.0 2 a_1))) True) (Eq (Not (r1 a)) True) % 6.62/6.78 Clause #55 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Not (r1 a)) True) (Eq (Eq a (skS.0 2 a_1)) True) % 6.62/6.78 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (Eq a (skS.0 2 a_1)) True) (Eq (r1 a) False) % 6.62/6.78 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq a (skS.0 2 a_1)) % 6.62/6.78 Clause #148 (by clausification #[8]): ∀ (a : Iota), % 6.62/6.78 Eq (Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 Y8)) (Exists fun Y18 => And (r1 Y18) (Eq Y8 Y18))) % 6.62/6.78 True % 6.62/6.78 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota), % 6.62/6.78 Eq % 6.62/6.78 (And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) % 6.62/6.78 (Exists fun Y18 => And (r1 Y18) (Eq (skS.0 10 a a_1) Y18))) % 6.62/6.78 True % 6.62/6.78 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (Exists fun Y18 => And (r1 Y18) (Eq (skS.0 10 a a_1) Y18)) True % 6.62/6.78 Clause #151 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) True % 6.62/6.78 Clause #152 (by clausification #[150]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 11 a a_1 a_2)) (Eq (skS.0 10 a a_1) (skS.0 11 a a_1 a_2))) True % 6.62/6.78 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 10 a a_1) (skS.0 11 a a_1 a_2)) True % 6.62/6.78 Clause #154 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 11 a a_1 a_2)) True % 6.62/6.78 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 10 a a_1) (skS.0 11 a a_1 a_2) % 6.62/6.78 Clause #156 (by forward demodulation #[154, 155]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 10 a a_1)) True % 6.62/6.78 Clause #157 (by superposition #[156, 58]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 10 a a_1) (skS.0 2 a_2)) % 6.62/6.78 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 10 a a_1) (skS.0 2 a_2) % 6.62/6.78 Clause #161 (by superposition #[158, 158]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 10 a a_1) (skS.0 10 a_2 a_3) % 6.62/6.78 Clause #173 (by clausification #[151]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 15 a a_1 a_2)) (r4 a (skS.0 15 a a_1 a_2) (skS.0 10 a a_1))) True % 6.62/6.78 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 15 a a_1 a_2) (skS.0 10 a a_1)) True % 6.62/6.78 Clause #175 (by clausification #[173]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 15 a a_1 a_2)) True % 6.62/6.78 Clause #177 (by superposition #[174, 161]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (r4 a (skS.0 15 a a_1 a_2) (skS.0 10 a_3 a_4)) True % 6.62/6.78 Clause #178 (by superposition #[175, 58]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (skS.0 15 a a_1 a_2) (skS.0 2 a_3)) % 6.62/6.78 Clause #179 (by clausification #[178]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 15 a a_1 a_2) (skS.0 2 a_3) % 6.62/6.78 Clause #182 (by superposition #[179, 179]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (skS.0 15 a a_1 a_2) (skS.0 15 a_3 a_4 a_5) % 6.62/6.78 Clause #183 (by clausification #[11]): Eq (Exists fun Y1 => And (Exists fun Y2 => And (r1 Y2) (r4 Y2 Y2 Y1)) (Exists fun Y3 => And (r1 Y3) (Eq Y1 Y3))) False % 6.62/6.78 Clause #184 (by clausification #[183]): ∀ (a : Iota), Eq (And (Exists fun Y2 => And (r1 Y2) (r4 Y2 Y2 a)) (Exists fun Y3 => And (r1 Y3) (Eq a Y3))) False % 6.63/6.80 Clause #185 (by clausification #[184]): ∀ (a : Iota), % 6.63/6.80 Or (Eq (Exists fun Y2 => And (r1 Y2) (r4 Y2 Y2 a)) False) (Eq (Exists fun Y3 => And (r1 Y3) (Eq a Y3)) False) % 6.63/6.80 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), Or (Eq (Exists fun Y3 => And (r1 Y3) (Eq a Y3)) False) (Eq (And (r1 a_1) (r4 a_1 a_1 a)) False) % 6.63/6.80 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (r1 a) (r4 a a a_1)) False) (Eq (And (r1 a_2) (Eq a_1 a_2)) False) % 6.63/6.80 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (r1 a) (Eq a_1 a)) False) (Or (Eq (r1 a_2) False) (Eq (r4 a_2 a_2 a_1) False)) % 6.63/6.80 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r4 a a a_1) False) (Or (Eq (r1 a_2) False) (Eq (Eq a_1 a_2) False))) % 6.63/6.80 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r4 a a a_1) False) (Or (Eq (r1 a_2) False) (Ne a_1 a_2))) % 6.63/6.80 Clause #191 (by destructive equality resolution #[190]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r4 a a a_1) False) (Eq (r1 a_1) False)) % 6.63/6.80 Clause #195 (by superposition #[191, 175]): ∀ (a a_1 a_2 a_3 : Iota), % 6.63/6.80 Or (Eq (r4 (skS.0 15 a a_1 a_2) (skS.0 15 a a_1 a_2) a_3) False) (Or (Eq (r1 a_3) False) (Eq False True)) % 6.63/6.80 Clause #200 (by superposition #[177, 182]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (r4 a (skS.0 15 a_1 a_2 a_3) (skS.0 10 a_4 a_5)) True % 6.63/6.80 Clause #355 (by clausification #[195]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 (skS.0 15 a a_1 a_2) (skS.0 15 a a_1 a_2) a_3) False) (Eq (r1 a_3) False) % 6.63/6.80 Clause #356 (by superposition #[355, 200]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) False) (Eq False True) % 6.63/6.80 Clause #359 (by clausification #[356]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 10 a a_1)) False % 6.63/6.80 Clause #360 (by superposition #[359, 156]): Eq False True % 6.63/6.80 Clause #361 (by clausification #[360]): False % 6.63/6.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------